Finite Group DatabasebetaFinite Group Databasebeta| order | 1024 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C42 · Schur multiplier (H2) = C221×C4 |
| direct product | C24×C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C26×C4 | C22 |
| commutator | C2 | C25×C42 |
| Frattini, cosocle | C23 | C27 |
| prime radical | C28 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C4 ◁ G | |
| LECS | G ▷ C23 ▷ C1 | |
597333 conjugacy classes of subgroups.
| transitive degree | μt(G) = 512 |
640 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×D4×C22⋊C4, C23×C4×#392, C23×#15124, … |
| maximal normal subgroup of | C24×D4×C22⋊C4, C23×C4×#392, C23×#15124, … |
| maximal quotient of | C22×#513545, C23×C4×#379, C23×C22⋊C42, … |
Past the SmallGroups library coverage — no SmallGroups id.